Prove that in any triangle the sum of squares of any two sides is equal to twice the square of half the third side together with twice the square of the median.

If the sum of squares of two sides is equal to square of third side then DeltaABC is

Prove that in a triangle if the square of one side is equal to the sum of the squares of the other two side then the angle opposite to the first side is a right angle.

Prove that in a triangle, if the square of one side is equal to the sum of the squares of the other two sides, then the angles opposite to the first side is a right angle.

Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals.

Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals.

Prove that the sum of the squares of the diagonals of parallelogram is equal to the sum of the squares of its sides.

Prove that in any parallelogram the sum of squares of the diagonals is twice the sum of the squares of two adjascent sides. Also show that the difference of the squares on two adjacent sides is equal to the rectangle contained by either diagonal and the projection of the other upon it.

Prove analytically that the sum of square of the diagonals of a rectangle is equal to the sum of squares of its sides.

Prove that three times the square of any side of an equilateral-triangle is equal to four times the square of the altitude.

Theorem 6.8 : In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.